I'd like to put a new headset on my commuter, but the lower cups of the current one have been installed at an angle (pic below), and I'm worried that this has reamed the head tube so that messing with the headsets would be a Bad Idea. Am I right?I can live with the current headset, but I'm putting a UK order together and it'd be nice to upgrade I can. The current headset lets water in at the top, pushing the grease out at the bottom (which you can see in the pic) and allowing the bearings to rust.

Most modern headsets (even the cheaper models) have a top race that goes over top of the upper cone to keep water out. Only the cheapest 1970s chromed steel headsets have top races that would let water in - they had an upwards-facing cup and the cone was screwed down from above. Your bike looks to be a more recent model than this. The grease coming out of the lower race may well be due to too much grease being packed in there - grease is generally water-proof and is unlikely to be washed out by water. Have you disassembled it and seen that the bearings are corroded?

The misaligned race could in all likelihood be corrected by disassembly and the use of some blocks of wood/metal and a good hammer blow to seat it in the correct alignment.

Riding bikes in traffic - what seems dangerous is usually safe; what seems safe is often more dangerous.

The bearings are corroded. This is the second time this has happened. The first time, the problem was found by the LBS who replaced the bearings and packed them with marine grease. The second time, I opened the headset myself maybe 18 months later, found the lower bearings had corroded again and repacked them myself with marine grease. Between these two services I had the problem with a noticeable smear of grease coming out the bottom.

It is a modern threadless set (bike's a 2010 model). Here's a pic of the top race:

As you can see the top race is divided into two concentric rings for some reason. I guess the water is entering through the gap between them.

A new set of bearings every year or so is obviously not a big deal, especially as the actual performance of the headset never seems to actually suffer, even when the bearings are corroded. But still, having a fit-a-forget headset would be nice.